In addition to the GW parameters \(\alpha \)  and \(\beta /H_{\ast }\)  and the nucleation temperature \(T_{n}\) ,
the GW spectrum also depends on the bubble wall velocity \(v_{w}\) , which is the expanding speed of the true vacuum.
It has been pointed out in Refs. [1]}, [2]} that it is the relative velocity between the wall and the plasma in the front (\(v_+\) ) rather than \(v_w\)  that should be used in the calculations of EW baryogenesis. For a strong EWPT,
the condition \(v_+\ll v_w\)  could be achieved, making it possible to generate a viable EW baryogenesis and a loud GW signal
in the same scenario. In this work, the bubble velocity \(v_w\)  is simply assigned to be around 1 for the calculations of GW spectra.
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